Flashcard 13 - Next Generation Advanced Algebra and Functions Flashcard Set for the ACCUPLACER Test

Exponents:

\[a^0 = 1\;,\;a \ne 0\] \[x^a \cdot x^b = x^{a + b}\] \[x^a \div x^b = x^{a - b}\] \[(x^a)^b = x^{a\cdot b}\] \[x^{-a} = \frac{1}{x^a}\]

Logarithms:

\[\log_b{1}=0\] \[\log_b{b}=1\] \[\log_b{x} + \log_b{y} = \log_b{xy}\] \[\log_b{x} - \log_b{y} = \log_b{\frac{x}{y}}\] \[\log_b{x^y} = y\log_b{x}\] \[\log_b{x} = \frac{\log_a{x}}{\log_a{b}}\]

\(x^a = y\) can be written as \(\log_x{y}=a\), with \(y > 0\), \(x > 0\), and \(x \ne 1\)

Logarithms and exponents share an inverse relationship. Consequently, some problems can be solved by rewriting in their inverted form and applying the appropriate properties of logarithms or exponents.